The Jackson Jammers are giving away bags and caps at their next game. The bags, b , cost them $10 each, and the caps, c , cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.(1 point)

Question

Responses

b+c=12,500; 10b+5c=2,000
b plus c equals 12,500 ; 10 b plus 5 c equals 2,000

b+c=2,000; 5b+10c=12,500
b plus c equals 2,000 ; 10 b plus 10 c equals 12,500

b+c=12,500; 5b+10c=2,000
b plus c equals 12,500 ; 5 b plus 10 c equals 2,000

b+c=2,000; 10b+5c=12,500

Answer 1

To model this situation with a pair of linear equations, we use the information given:

1. Let \(b\) be the number of bags given away and \(c\) be the number of caps. They plan to give away a total of 2,000 items, which gives us the first equation: \[ b + c = 2000 \]

2. The cost of the bags is $10 each, and the cost of the caps is $5 each. They have a budget of $12,500 for these items, leading to the second equation: \[ 10b + 5c = 12500 \]

The correct pair of linear equations that model this situation is: \[ \begin{align*} b + c &= 2000 \ 10b + 5c &= 12500 \end{align*} \]

So the correct answer is: b + c = 2000; 10b + 5c = 12500